If $m \angle QPS = 180^\circ$ and $m \angle QPR = 102^\circ$, what is $m \angle RPS$, in degrees? $102^\circ$ $P$ $Q$ $S$ $R$
Answer: From the diagram, we see that $\angle QPR$ and $\angle RPS$ are supplementary angles. Therefore, $m \angle QPR + m \angle RPS = 180^\circ$ Thus, $m \angle RPS = 180^\circ - m \angle QPR = 180^\circ - 102^\circ = 78^\circ$.